WLF 448: Fish & Wildlife Population Ecology
Lab Notes 7

In-class Exercise:

Band Recovery

(Survival Estimation)

 

We will be using a program called MARK for this exercise. MARK is a very powerful program that utilizes current modeling techniques and model selection procedures. This program can handle most types of marking data. Survival estimation is the main focus of the program although it does have the capabilities to perform population estimation. For this exercise we will analyze a band recovery data set on wood ducks using some very simple models. The analysis capabilities of this program go far beyond the scope of this lab.

I. Copy the input files from the class directory to your personal directory:

The file you need to copy for the in class exercise is in the directory k:\wlf\448\MARK\ and is called slvm_exer.inp. The dataset for the homework is mallard.inp in the same directory.  If you encounter problems in the early stages of the exercise, you may find that copying the entire MARK folder from the k: drive to your workspace alleviates the problems.

 

II. Starting a project:

Open MARK by clicking on programs under the start menu, then on Analytical, and then select MARK 4.2.

 

    1. First you need to start a new project or open an existing project. Click on the

      2. file drop down menu and then click new. You should now be in the ‘File

      Specifications Window.’

    2. Select the ‘Data Type’. We will be using band recovery data so select

      3. "Recoveries Only."

    3. Enter a Title for your data set.
    4. Under ‘Encounter Histories File Name:’ either type the directory and filename or select ‘click to select file.’ Then find the desired file in the directory where you saved it and select the file.(Remember: slvm_exer.inp for in-class, mallard.inp for homework)

      5.  

    5. Once you have selected the file, view it by clicking view file. Go through the recovery matrix and be sure you understand the structure of the file. Close this editor when you are done (Go to file and then exit). Note the classes and number of recovery events - you will need this info in the next steps.
    6. Change the ‘Encounter Occasions’ to the appropriate number for your data set. It defaults to 5 but this is in no way indicative of the encounter occasions of your data set. How many years were bands recovered (i.e. How many columns are in the matrix in the input file?)
    7. Change the ‘Attribute Groups’ to the appropriate number for your data set. How many groups do you have? It defaults to one but does this does not indicate the true number for your data set. (Hint: How many classes were banded and recovered? Hint 2: Notice that the in-class exercise has Adult and Young classes whereas the homework dataset has Males and Females - Labelling your groups at this stage will help later.)
    8. We will not use individual covariates or strata for this exercise.
    9. Once you have properly specified your analysis click ‘OK.’
    10. Click ‘OK’ when the program tells you it created a dbf file.

III. Running Models

    1. You should now see the parameter index matrix (PIM) for the survival parameters of the first group. We need to look at all of the PIM’s. There will be one PIM for survival for each group and one PIM for recovery for each group. Thus, we will have a total of 4 PIM’s for this analysis.
    2. To open the other 3 PIM’s click on the ‘PIM’ drop down menu and select "Open Parameter Index Matrix." Then ‘select all’ and then ‘OK.’ All 4 PIM’s should now be open. (See Model Construction for explanation of PIM’s)
    3. Examine the PIM’s and make sure the parameter indexing is consistent with the s(g*t) r(g*t) model structure.
    4. Then select ‘Run’ from the drop down menu and select ‘Current Model.’
    5. You should now see the ‘Setup Numerical Estimation Run’ screen.
    6. Type in the model name; s(g*t)r(g*t).
    7. Change the ‘link function’ to "Logit." The link functions transform the data for the numerical estimation procedure. We will only use the "Logit."
    8. Leave everything else set as the default and select ‘Ok to Run.’
    9. A message will pop-up asking if the identity matrix should be used. This is a matrix with 1’s on the diagonal and 0’s everywhere else. Select ‘Yes.’
    10. The model estimation will scroll past on the screen and then the model results will appear as a tab at the bottom of the screen. Select the results file by clicking on the ‘Results’ tab at the bottom of the screen.
    11. The results will appear with a message asking if you want to append the results to the database. Select ‘Yes.’
    12. In the ‘Results Browser’ you should see the ‘model name’, AICc, Delta AICc, AICc Weight, Number of parameters, and the deviance. More on these after we have run all the models.
    13. To view the estimates select the fourth tool bar button from the left in the ‘Results Browser.’
    14. The parameter column corresponds to the parameter number you indexed in the PIM’s. (i.e. the 1st set of parameters estimate survival for adults/males for each year of recovery, the next set are survival estimates for juveniles/females, then the next set are recovery rates for adults/males, and the last set are recovery rates for juveniles/females.) Also note that there is a standard error and 95% confidence interval for each estimated parameter. (Note: In the in-class example there should be 36 parameters corresponding to 36 unique values in the PIM’s.)
    15. Close this notepad (File—Exit) (Note: you could print these estimates)
    16. Now you need to run 3 more models. [s(.t)r(.t)], [s(g.)r(g.)], and [s(..)r(..)]
    17. To do this you need to re-parameterize the PIM’s. (There are other ways to do this) You will notice that all the PIM’s are still open behind the ‘Results Browser.’
    18. Re-parameterize the PIM’s to reflect the structure of the s(.t)r(.t) model and follow steps 4-15. (Hint: the survival PIM’s should be time dependent but should not be dependent on sex. They should look indentical, using the same exact numbers.)
    19. You can quickly change numbers (PIM’s) by changing the first cell in the PIM to the desired number. Then go to the ‘Initial’ drop down menu and select either ‘Time’ (to get time specific variation) or ‘Constant’ (to get constant rates across recovery periods).
    20. After running this model and viewing the results, re-parameterize the PIM’s to run the s(g.)r(g.) model and follow steps 4-15. (Hint: this model has constant survival and recovery across recovery occasions but these rates are different between groups.)
    21. After running this model and viewing the results, re-parameterize the PIM’s to run the s(..)r(..) model and follow steps 4-15. (Hint: this model has constant survival and recovery rates across all recovery occasions and groups.)
    22. Now you should have the results of 4 models in the ‘Results Browser.’
    23. Think of how else you might parameterize a model. What are the biologically reasonable possibilities? MARK would allow you to re-parameterize this model in many more ways. You could even account for weather or environmental variables or weight the estimates by rainfall, temperature, or some other relevant variable.

 

IV. Interpreting the Results

    1. Current statistical theory would suggest that you can select the most applicable model based on information criteria (AIC). Thus, the most appropriate model of those that you just ran would be the one with the lowest AIC.
    2. Compare the order of preference of models based on AIC to their corresponding deviance. Deviance is essentially a measure of fit, or how well the estimated model compares to the data. It is possible that a model with fewer parameters could be the selected model by AIC, but have a greater deviance than other models.
    3. We can also compare "nested" models using likelihood ratio tests. A "nested" model is one that is constrained from a more complex situation. The null hypothesis for this test would be that the simpler model (model with fewer parameters) is as likely to explain the variation in the data as the more complex model.
    4. To run the likelihood ratio test select ‘LR Tests’ under the ‘Tests’ drop down menu.
    5. Then click ‘Select All’ to perform all likelihood ratio tests. Then click ‘OK.’ Note: doing this may result in likelihood ratio tests that are not valid (not tests of nested models). Thus, before interpreting a test make sure it is valid. In the program this test appears as ‘reduced model’ (simplest) compared to the ‘general model’ (more complex model).
    6. You can print these tests by selecting ‘Print’ under the file drop down menu in this notepad.
    7. When you are done with these results exit the notepad and return to the ‘Results Browser.’
    8. To print the ‘Results Browser’ click on the 7th toolbar button from the left on the ‘Results Browser’ toolbar. This will open the results browser into a notepad where you can select ‘Print’ under the ‘File’ drop down menu.
    9. The Delta AIC is the difference in the AIC value of each model compared to the model with the lowest AIC.
    10. The AIC Weight, weights the Delta AIC value for each model which is a method to explain how much "better" one model is compared to another.
    11. There are many other statistical tests that MARK will perform but we will leave those for the ambitious and mathematically inclined.

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Revised: 25 August 2011